This approach is present in literature. In [1]} (see also [2]}) E. D'Aniello and T.H. Steele proved that the family \(A[0,1]^d\)  is a meager subset of \(K([0,1]^d)\) , for every \(d\in \mathbb {N}\)  (see also [3]} where this fact is proved, however the statement of [3]} is false). In [5]} and [6]}, independently, it is shown that the same holds for the family \(A_w[0,1]^d\) . Moreover, the result about attractors for classical iterated function systems has been strengthened in [6]} by showing that \(A[0,1]^d\)  is even smaller – it is a \(\sigma \) -lower porous subset of \(K([0,1]^d)\) . The question about \(\sigma \) -lower porosity of \(A_w[0,1]^d\)  is still open (see [6]}).
